Mapping Hebbian Learning Rules to Coupling Resistances for Oscillatory Neural Networks.

Aida Todri-Sanial,Corentin Delacour

doi:10.3389/fnins.2021.694549

Abstract

Oscillatory Neural Network (ONN) is an emerging neuromorphic architecture with oscillators representing neurons and information encoded in oscillator's phase relations. In an ONN, oscillators are coupled with electrical elements to define the network's weights and achieve massive parallel computation. As the weights preserve the network functionality, mapping weights to coupling elements plays a crucial role in ONN performance. In this work, we investigate relaxation oscillators based on VO2 material, and we propose a methodology to map Hebbian coefficients to ONN coupling resistances, allowing a large-scale ONN design. We develop an analytical framework to map weight coefficients into coupling resistor values to analyze ONN architecture performance. We report on an ONN with 60 fully-connected oscillators that perform pattern recognition as a Hopfield Neural Network.

Highlights

Coupled oscillators have been studied for decades by scientists to describe natural phenomena (Winfree, 1967) such as the synchronization of pacemaker cells responsible for the heart beating, the synchronous behavior of insect populations, or to model neuronal activity
Unlike most Artificial Neural Networks (ANN) where signals of interest are amplitudes, Oscillatory Neural Network (ONN) consists of N VO2-oscillators coupled by resistances where the final result is given by N-1 phase relations to a reference oscillator (Corti et al, 2018)
We demonstrate the effectiveness of the proposed mapping function (22) to design a 60-ONN architecture for pattern recognition as in Hopfield Neural Networks (HNN)

Summary

Introduction

Coupled oscillators have been studied for decades by scientists to describe natural phenomena (Winfree, 1967) such as the synchronization of pacemaker cells responsible for the heart beating, the synchronous behavior of insect populations, or to model neuronal activity. Oscillator interactions have been shown to describe memory mechanisms and other cognitive processes in the brain (Fell and Axmacher, 2011) To characterize this variety of natural oscillations, several mathematical models (Acebrón et al, 2005; Izhikevich and Kuramoto, 2006) have been developed to explain the synchronization and phase relations in groups of coupled oscillators. Their massive parallel computing capability has been proved by Hoppensteadt and Izhikevich (2000), Vassilieva et al (2011), and Parihar et al (2017) and has raised interest in designing ONN as hardware accelerators for Artificial Neural Networks (ANN) by encoding neurons’ activation in the phase between oscillators. To design a competitive ONN at a large scale, a design framework is needed to establish a formalism on how to perform computations with ONN and compare its energy efficiency with ANNs running on digital processors

Methods

Results

Conclusion